Question

Prove with a neat diagram that the radius
of curvature of a spherical mirror is twice
its focal length.​

Answer 1

Explanation:

Let us consider MM’ as small aperture concave mirror. the line through centre of curvature C is perpendicular to the mirror.

Applying law of reflections

∠OMC = ∠CMF (angle of incidence = angle of reflection)

∠MCF = ∠OMC (alternate angle)

Hence, ∠MCF = ∠CMF

So, CF = MF

Since aperture of mirror is very small, M is very near P and we can put

CF = FP

PC = 2PF

C = 2f

Hence proved.

Hope it helps.